For a given cusped 3-manifold \(M\) admitting an ideal triangulation, we describe a method to rigorously prove that either \(M\) or a filling of \(M\) admits a complete
hyperbolic structure via verified computer calculations. The key ingredients of our method are the interval arithmetic and the Krawczyk Test. These techniques represent an
improvement over existing algorithms as they are faster while accounting for error accumulation in a more direct and user friendly way.

For a full list of the packages required and a instructions for more architectures, see the README.txt file associated to the download.

To install hikmot, use the command;

sudo python setup.py install

We can also specify the folder to install by "--prefix" e.g. ("~" is the home directory)

python setup.py install --prefix=~

It seems that Mac 10.9 (Xcode 5.1 or later) uses a new compiler clang that performs a little differently than gcc. Users might experience the following error:
clang: error: unknown argument: '-mno-fused-madd'
The reason of this error is found in the Xcode Release Notes,
"The Apple LLVM compiler in Xcode 5.1 treats unrecognized command-line options as errors. This issue has been seen when building both Python native extensions and Ruby Gems, where some invalid compiler options are currently specified."

This will return "True" for any valid triangulation of a hyperbolic manifold and "False" otherwise. The flag "True" turns on verbose reporting of the
verify_hyperbolicity function. For verifying large sets of manifolds, such as a census, it is recommended this flag be set to "False".

That's it! We just showed the mainfold 'm004', aka the figure 8 knot complement, is hyperbolic.

We prepare codes to verify census manifolds. See Theorem 6.1 and Theorem 6.2 of our paper for details.

By VerifyCuspedCensus.py, one can verify the hyperbolicity of manifolds in OrientableCuspedCensus :
P. Callahan, M. Hildebrand and J. Weeks, A census of cusped hyperbolic 3-manifolds, Math. Comp. 68 (1999), no. 225, 321–332.
To run the code, install hikmot and

python VerifyCuspedCensus.py

Then, the expected output of this code is:
Out of 17661 manifolds in the OrientableCuspedCensus, 17661 have been proven to be hyperbolic and 0 have not.

We need some geometric techniques to produce triangulations that hikmot can verify the hyperbolicity of manifolds in the census, OrientableClosedManifold :
C. Hodgson and J. Weeks, Symmetries, isometries and length spectra of closed hyperbolic three-manifolds, Experiment. Math. 3 (1994), 261--274.
Instead of explaining the technique, we have prepared the set of triangulations in the file: ClosedManifolds.zip (approx. 7MB).
Decompress the .zip file at the same folder as hikmot.py.
If you are interested in the technique we used to produce ClosedManifolds, see Theorem 6.2 of our paper.
The codes that apply the technique are available via email.
The code VerifyClosedCensus.py checks if each manifold in ClosedManifolds is hyperbolic and
isometric to the corresponding census manifold (by is_isometric_to() function of SnapPy).
Running the code should take under 10 minutes and can be called by the following:

python VerifyClosedCensus.py

Then output will be:
You will probably fail proving Closed3.tri to be hyperbolic, this is 'm007(3,1)' and we need to take a cover for this manifold.
Failed proving the hyperbolicity of Closed3.tri aka m007(3,1).
Out of 11031 manifolds in OrientableClosedCensus,11030 manifolds have been proven to be hyperbolic! 1 error.
Verified the hyperbolicity of m007~cyc~0(1,0)(1,0)(1,0), a cover of m007(3,1).
There was one bad manifold. It has been verified and 0 remain.

This completes the verification of the hyperbolicity of all manifolds in OrientableClosedCensus.

The authors would like to thank Mark Bell, Marc Culler, Nathan Dunfield, Craig Hodgson, Sadayoshi Kojima, and Bruno Martelli for a number of helpful conversations. N. H would like to thank Nihon University and the Tokyo Institute of Technology for graciously hosting him during a visit to Japan in the early stages of this project. Finally, for the remainder of this project, N. H has been supported by the Max Planck Institute for Mathematics and Australian Research Council Discovery Grant DP130103694. K. I was partially supported by Grant-in-Aid for Young Scientists (B), No. 23740061, Ministry of Education, Culture, Sports, Science and Technology, Japan. The work of H. M was supported by JSPS Research Fellowship for Young Scientists. S. O and A. T were partialy supported by the CREST, JST project tilted Establishment of Foundations of Verified Numerical Computations for Nonlinear Systems and Error-free Algorithms in Computational Engineering.
Finally, the authors wish to thank Tokyo Institute of Technology, the University of Texas Math Department, and Waseda University for providing computer support for this project.